The sugar content of the syrup in canned peaches is normally distributed. Suppose that the variance is thought to be σ2=18 (milligrams)2. A random sample of n=10 cans yields a sample standard deviation of s=4.8 milligrams. Part 1 (a) Test the hypothesis H0:σ2=18 versus H1:σ2≠18 using α=0.05 Find χ02 .

The degrees of freedom are:

Now we can calculate the critical value taking in count the alternative hypotheis we have two values:

Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18

Step-by-step explanation:

Information given

represent the sample size

represent the confidence level  

represent the sample variance obtained

represent the value to verify

System of hypothesis

We want to verify if the true variance is different from 18, so the system of hypothesis would be:

Null Hypothesis:

Alternative hypothesis:

The statistic would be given by:

And replacing we got:

The degrees of freedom are:

Now we can calculate the critical value taking in count the alternative hypotheis we have two values:

Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18

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step-by-step explanation:

sorry no step by step